Confusion with the centrifugal foce and potential energy

[tolove]

When we release a suspended object, we recover the potential energy due to gravity as the object travels back through the height raised.

When we release an extended spring, we recover the potential energy as the object travels back through the distance stretched.

But when we release a rotating object, how is the centrifugal potential energy recovered?

I know that if we integrate the centrifugal force over the radius, we can numerically recover the potential, but I still feel as if I am missing something.

Thank you for your time!

 

[A.T.]

But when we release a rotating object, how is the centrifugal potential energy recovered?

Centrifugal force and centrifugal potential energy exist only in a rotating frame of reference. If you release on object that was initially at rest in the rotating frame, it will gain speed in the rotating frame, converting centrifugal potential energy into kinetic energy.

In the inertial frame it's of course just moving at constant speed, not gaining any kinetic energy.

 

[sweet springs]

Hi.　
I imagined your case hammer throw with chain replaced by spring.　　Spring is extended by rotation of the player. When he releases the hammer, weight and spring make vibration.　　Spring gets elastic energy by downing weight in centrifugal potential. Spring elastic energy convert to vibration　energy by the release.

 

[jbriggs444]

The scenario I imagine is different. Possibly we need to ask OP to clarify things.

Suppose that you are standing on the floor of a rotating space station. You have a mass on a string and allow it to drop from table to floor while harvesting the energy as the string pays out. For a 1 kg object dropping 1 meter under 1 g of artificial gravity you could harvest ~10 Joules of centrifugal potential energy in this manner. You could use this to partially recharge a battery.

But if one adopts a non-rotating frame of reference and looks at the same scenario, there is a conundrum. There is no centrifugal potential to harvest. 10 Joules of energy went into charging a battery. The object moved 1 meter farther from the center of rotation and ended with more kinetic energy than it started. Where did the energy come from?

It came from the rotation of the space station. We can walk through the details that reconcile the two points of view if OP is interested.